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Accurate and Efficient Spectral Methods for Elliptic PDEs in Complex Domains

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Abstract

We develop accurate and efficient spectral methods for elliptic PDEs in complex domains using a fictitious domain approach. Two types of Petrov–Galerkin formulations with special trial and test functions are constructed, one is suitable only for the Poisson equation but with a rigorous error analysis, the other works for general elliptic equations but its analysis is not yet available. Our numerical examples demonstrate that our methods can achieve spectral convergence, i.e., the convergence rate only depends on the smoothness of the solution.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA

    Yiqi Gu & Jie Shen

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  1. Yiqi Gu
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  2. Jie Shen
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Correspondence to Jie Shen.

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This work is supported in part by NSF Grant DMS-1720442 and AFOSR Grant FA9550-16-1-0102.

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Gu, Y., Shen, J. Accurate and Efficient Spectral Methods for Elliptic PDEs in Complex Domains. J Sci Comput 83, 42 (2020). https://doi.org/10.1007/s10915-020-01226-9

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